SOLUTION: Factor the following polynomials completely making use of the given zero G(x)=x^3-(1-i)X^2-(8-i)x+(12-6i);2-i is a zero

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Factor the following polynomials completely making use of the given zero G(x)=x^3-(1-i)X^2-(8-i)x+(12-6i);2-i is a zero      Log On


   

Question 370375: Factor the following polynomials completely making use of the given zero
G(x)=x^3-(1-i)X^2-(8-i)x+(12-6i);2-i is a zero
Answer by jsmallt9(3759) About Me  (Show Source):
You can put this solution on YOUR website!
G%28x%29=x%5E3-%281-i%29x%5E2-%288-i%29x%2B%2812-6i%29
If 2-i is a zero, then (x-(2-i)) or (x - 2 + i) is a factor of G(x). We need to find the other factor and for this we can use Synthetic Division:
2-i |   1  -1+i  -8+i  12-6i
-----       2-i   2-i -12+6i
       ----------------------
        1   1    -6     0

Te remainder is zero so 2-i is indeed a factor. And the rest of that row of numbers, 1 1 -6, tells us the other factor: 1x%5E2+%2B+1x+-+6. So now
G%28x%29+=+%28x-2%2Bi%29%28x%5E2%2Bx-6%29
The second factor is a trinomial that is easily factored giving:
G%28x%29+=+%28x-2%2Bi%29%28x%2B3%29%28x-2%29%29
G(x) is now fully factored.